An alternate method is to recognize that for a string fixed at both ends the wavelength is 2 times the length of the string. In that case you have a wavelength of 2 m.

The relationship between the string tension F(T), the m/L ratio and the velocity of the wave is: F(T) = m/L * v^2

Solving for the velocity gives 31.62 m/s.

Since v = frequency * wavelength; 31.62 m/s divided by 2 m = 15.81 Hz as the fundamental frequency.

As you can see, in physics there is often more than one way to end up with the correct answer.